Visualization of a Hyperbolic Structure in Area Preserving Maps

A. Giorgilli, Dipartimento di Matematica, Universit\`a degli Studi di Milano,
   via Saldini 50, 20133 Milano, Italy

V. F.Lazutkin, Physics Department, St.-Petersburg State University,
   Ulyanov str. 1, kor.1, Petrodvorets, St.-Petersburg, 198904, Russia

C. Sim\'o, Departament de Matem\`atica Aplicada i An\`alisi,
   Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain

Abstract

We present a simple method which displays a hyperbolic structure in the phase
space of an area preserving map. The method is  illustrated  for the
case of the Carleson standard map. As it follows from our experiments,
the structure of the chaotic zone for the standard map is different from
the one found for the systems of Anosov type.
